Page 185 - Theory and Design of Air Cushion Craft

168 Stability

To simplify the calculation, we assume that one fan supplies the flow rate to both
left and right cushions instantaneously and the pressure in both left and right
cushions is equal. Thus the characteristics of cushion pressure and air leakage from
bag holes can be expressed as
= P t- 3G?
P d
^cr = Pt - E rQl (4.23)
where (?,, Q r, are the flow rates from left/right cushion, E b E T the loss coefficient of bag
holes in left/right cushion and P d, P CT the pressure in left/right cushion.
From the flow rate continuity equation, we have

6 = a + a
Q^ = & + a,
a = Gar - 81, (4-24)
where Q el, Q er are the flow rates leaking from left/right cushion and Q ]r, the cross-flow
from left cushion to right cushion, can be written as
a r = W(2/A,lA:i - /^crlsgn (p d - p CT)A eg (4.25)
where </> is the flow rate coefficient and A eg the leakage area of cross-flow. A eg, Q d and
Qer in the above equations are related to the air leakage gap; they are a function of
heeling angle 9.
In the case where one side contacts the ground, the cushion area of this side kneel-
ing down may be determined as follows. Figure 4.31 shows the contacting point of the
skirt with the ground, d, in the case of a craft where the skirt touches but is not
deformed. This will be shifted to d' in the case of heeling craft due to the skirt kneel-
ing down, the cushion area at this side (skirt kneeling down) will increase in order to
provide the restoring moment.
The contacting point is related to the outer surface inclination angle of the skirts,
a. The righting moment is inversely proportional to a. These effects have been con-
sidered in equation (4.21). The equation group in this section is called the coupled sta-
bility equation for heeling and heaving of ACVs, which is very similar to that for SESs.
In the case where the heeling moment (force), principal dimensions of the craft and
the leading particulars for fans, skirts and cushion are given, then the parameters such
as P cr, P t, Q, Q e[, Q er, Q h can be solved with aid of a computer and the expressions
(4.20)-(4.25). The heeling angle 9 as well as the vertical position of CG (£ g) can also
be obtained.
Figure 4.33 shows a typical curve of static transverse stability of an ACV hovering
on a rigid surface. It can be seen that the curve is nonlinear at larger heel angles, due
to the nonlinear factors of fan characteristics and ground contact and deformation of
skirts.

4.5 Factors affecting ACV transverse stability

Based on the equations mentioned above, one can discuss the effect of the various para-
meters on the static transverse stability of an ACV. However, the errors of calculation
are rather large since no account is taken of the deformation of skirts caused by the